Angle of a semicircle on a ramp

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Homework Help Overview

The problem involves a semicylinder on a rough inclined plane, with specific parameters such as mass, radius, angle of inclination, and coefficient of static friction. The original poster attempts to determine if the semicylinder will slide down the plane and, if not, to find the angle of tip of its base.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equilibrium positions and the forces acting on the semicylinder. There are inquiries about the accuracy of force diagrams and the intersection of the normal force with the base of the semicylinder. Some participants express uncertainty about their understanding of equilibrium.

Discussion Status

The discussion includes attempts to clarify the problem and explore different approaches to finding the angle of tip. Some guidance has been offered regarding the drawing of forces, but there is no explicit consensus on the methods being used. The original poster has indicated progress in their understanding.

Contextual Notes

Participants mention the need for accurate diagrams and the challenges of applying trigonometric principles in this context. There is an acknowledgment of the original poster's previous calculations regarding the sliding condition of the semicylinder.

stewood
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Homework Statement


The semicylinder of mass m and radius r lies on the rough inclined plane for which ϕ = 10∘ and the coefficient of static friction is μs = 0.3. Determine if the semicylinder slides down the plane, and if not, find the angle of tip θ of its base AB

Homework Equations


f=uN

The Attempt at a Solution


I think this requires some weird trigonemetry... I already calculated that the cylinder does not slide down but I cannot calculate the angle of theta
upload_2015-11-20_8-51-14.png
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stewood said:
but I cannot calculate the angle of theta
What did you try so far?
What do you know about equilibrium positions?
 
Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?
 
mfb said:
What did you try so far?
What do you know about equilibrium positions?
I've tried a few different triangles, but I can't figure it out. I know nothing about equilibrium positions.
 
haruspex said:
Your drawing of the forces could be a little more accurate. Where will the line of action of the normal force intersect AB?
How can I calculate that?
 
Never mind, I figured it out. In case your curious you use the law of sines...
 

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